There are a lot of bad restaurants in Times Square, and the neighborhood doesn't excel in the cuisines your kids will eat. If they ate Chinese, Thai, Mexican, Japanese, etc. you'd have a lot more excellent options--ones that people from other neighborhoods come to Times Square/Midtown for.

Can you get out of Times Square, even for a night or two?

Pizza: I'm not a huge fan of John's in Times Square, choose another from the list thegforceny linked to.

Italian: I love Esca but it's pricey and seafood oriented, check out the menu online, it really depends how picky your kids are and if you meant Italian American vs. Italian.

Steak: Make a reservation for Keens and check out the menu online, great history and service and atmosphere, not cheap though. One of the few places serving a mutton chop as well.

Burgers: I prefer Shake Shack and Schnipper's over 5 Napkin, Bill's, and burger joint in the Parker Meredien hotel.

Also, I think some bakeries might be a nice kid-friendly option. Try Bouchon Bakery, Jacques Torres, or Magnolia, all in Rockefeller Center, Momofuku Milk Bar is also a short walk away on 5th Avenue near many department stores. The wichcraft in Rockefeller Center has good baked goods as well.

And the Plaza Hotel has a high quality food court, which seems like an easy option to me when everybody is tired and nobody wants to eat the same thing. It's closer to Central Park than Times Square but I though I'd mention it if you're sightseeing.